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Published online by Cambridge University Press: 19 July 2016
The exact numerical solution of the simplest non-linear equation from the hierarchy of non-linear equations for the averaged Green function shows that such solution allows to calculate the diffusivity and α-effect coefficient with a good accuracy for an arbitrary spectra of turbulence for all values of the characteristic parameter. It is derived also the improved equation describing the evolution of admixture fluctuations in a turbulent medium which takes into account the non-linear equation for the averaged Green function.